Dirac quantum walks on triangular and honeycomb lattices

In this paper, we present a detailed study on discrete-time Dirac quantum walks (DQWs) on triangular and honeycomb lattices. At the continuous limit, these DQWs coincide with the Dirac equation. Their differences in the discrete regime are analyzed through the dispersion relations, with special emphasis on Zitterbewegung. An extension which couples these walks to arbitrary discrete electromagnetic field is also proposed and the resulting Bloch oscillations are discussed.